Answers
Answer:
X = [tex]\sqrt{2}[/tex] , Y = 3 , Z = 10
Step-by-step explanation:
using Pythagoras' identity in all 3 right triangles
X² = 1² + 1² = 1 + 1 = 2 ( take square root of both sides )
X = [tex]\sqrt{2}[/tex]
middle triangle
Y² = 1² + X² = 1 + ([tex]\sqrt{2}[/tex] )² = 1 + 2 = 3
triangle on right
Z² = 1² + Y² = 1 + 3² = 1 + 9 = 10
Related Questions
A gardener wants to fence in her plot in two equal rectangular sections. If she has 54 yards of fence and the area of the entire plot is 108 square yards, find the possible dimensions of the garden.
Answers
Considering the perimeter and the area of the rectangle, the possible dimensions are of 22.11 yards and 4.89 yards.
What are the area and the perimeter of a rectangle?Considering a perimeter of length l and width w, we have that:
The area is lw.The perimeter is 2(l + w).In this problem, considering the amount of fencing as the perimeter, and the area, we have that:
2(l + w) = 54 -> l + w = 27 -> w = 27 - l.lw = 108.Then:
l(27 - l) = 108
l² - 27l + 108 = 0.
Which is a quadratic equation with coefficients a = 1, b = -27, c = 108, then:
[tex]\Delta = b^2 - 4ac = (-27)^2 - 4(1)(108) = 297[/tex]
[tex]x_1 = \frac{27 + \sqrt{297}}{2} = 22.11[/tex]
[tex]x_2 = \frac{27 - \sqrt{297}}{2} = 4.89[/tex]
Then, the possible dimensions are of 22.11 yards and 4.89 yards.
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Can someone help me with this question please
Answers
The congruent parts of the triangle are:
< A ≅ <X
<B ≅ <Z
<C ≅ <Y
AB ≅ XZ
AC ≅ AY
BC ≅ ZY
BCA ≅ ZYX
What are the congruent parts?The shape in the image are right angle triangles. A right angle triangle is a triangle that has three sides and a right angle. Congruent triangles are triangles that have the same size and the angles.
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Evaluate i=∫c(sinx 9y)dx (3x y)dy for the nonclosed path abcd in the figure. A=(0,0),b=(4,4),c=(4,8),d=(0,12)
Answers
The value of the integration for a non closed path abcd will be -88
What is cyclic integration?
Cyclic integration is the integration over a closed loop.Close the path by connecting D to A. Then by Green's theorem, the integral over the closed path ABCDA - which I'll just abbreviate C - is
[tex]\oint_c(Sin(x)+9y)dx+(4x+y)dy\\\\\\[/tex]
[tex]=\int\int \dfrac{\partial (4x+y)}{\partial x} -\dfrac{\partial (Sin(x)+9y)}{\partial y}dxdy[/tex]
[tex]=-5\int\int dxdy[/tex]
(where int(C ) denotes the region interior to the path C )
The remaining double integral is -5 times the area of the trapezoid, which is
[tex]-5 \int\int dxdy=\dfrac{-5}{2}\times (12+4)\times 4=-160[/tex]
To get the line integral you want, just subtract the integral taken over the path DA. On this line segment, we have x = 0 and dx = 0, so this integral reduces to
[tex]\int _{DA} ydy=\int\limits^0_{12} y dy=-\int\limits^{12}_0ydy =-72[/tex]
Then
[tex]\int_{ABCD}9Sin(x)+9y)dx+(4x+y)dy=-160-(-72)=-88[/tex]
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I need to know how to solve these using the box method
Answers
Answer:
5. (2x-3)(3x+2)
6.(x-8)(2x-5)
7.(5x-2)(2x+1)
8.(4x+3)(x+3)
Step-by-step explanation:
example on how to solve this in not how you solve your questions
2x times x = 2x2
2x times 2 = 4x
5 times x = 5x
5 times 2 = 10
The factors are (2x + 5) and (x + 2), so 2x2 + 9x + 10 = (2x + 5) × (x + 2)
4x and 5x are interchangeable, so you could put 5x in the first row and 4x in the second row and still get the same answer.
Which of the following terms best describes the red line segment in the
ellipse shown below?
O A. Center
O
B. Focus
O
C. Minor axis
D. Major axis
Answers
The term that best describes the red line segment of the ellipse is minor axis . C
What is an eclipse?
An eclipse can be defined as an astronomical event that occurs when an object or spacecraft is obscured as the shadow of another body passes or when another body pass between it and an observer.
The axis of an eclipse could major or minor.
The minor axis of an ellipse is the line that contains the shorter part of the two line segments about which the ellipse is symmetrical. It is perpendicular to the major axis and passes through the center of the axis.
Therefore, the term that best describes the red line segment of the ellipse is minor axis . C
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One figure models 1/4 as 4 of 12 equal parts of a whole. The other models 1/3 as 1 of 3 equal parts of a whole. What is true about the equal parts for the two fractions?
Answers
The correct option for this questions is Option C
Equivalent Fractions for 4/12:
1/3, 2/6, 3/9, 4/12, 5/15, 6/18, 7/21, 8/24, 9/27, 10/30, 11/33, 12/36, 13/39, 14/42, 15/45, 16/48, 17/51, 18/54, 19/57, 20/60, and so on ...
How do you find equivalent fractions?Two frations are equivalent when they have the same value when written in lowest terms. The fraction 8/24 is equal to 1/3 when reduced to lowest terms. To find equivalent fractions, just multiply the numerator and denominator of that reduced fraction (1/3) by any interger number, ie, multiply by 2, 3, 10, 30.
2/6 is equivalent to 4/12 because 1 x 2 = 2 and 3 x 2 = 63/9 is equivalent to 4/12 because 1 x 3 = 3 and 3 x 3 = 94/12 is equivalent to 4/12 because 1 x 3 = 4 and 3 x 3 = 12Equivalent fractions may look different, but when you reduce then to the lowest terms you will get the same value. If any fraction is not reduced to lowest terms, you can get other equivalent fractions just dividing both numerator and denominator by the same number.
Thus, option c is your answer
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I) find, in terms of π, the curved surface area of a cone with circular base diameter 10cm and height 12cm.
Ii) if the cone is made of paper, and the paper is flattened out into the sector of a circle, what is the angle of the sector?
[tex]\pi[/tex]
Answers
Answer:
[tex]\huge\underline{\red{A}\blue{n}\pink{s}\purple{w}\orange{e}\green{r} -}[/tex]
( i )
given - a cylinder with base diameter = 10 cm ! And , height = 12 cmTo find - CSA of conenow ,
since diameter = 10 cm
[tex]\implies \: radius = \frac{10}{2} = 5 \: cm \\ [/tex]
now ,
[tex]slant \: height \: ( \: l \: ) = \sqrt{h {}^{2} + r { }^{2} } \\ \\ \implies \: \sqrt{(12) {}^{2} + (5) {}^{2} } \\ \\ \implies \: \sqrt{144 + 25} \\ \\ \implies \: \sqrt{169} \\ \\ \implies \: 13 \: cm[/tex]
now ,
[tex]CSA \: of \: cone = \pi \: \times r \times l \\ \\ \implies \: \pi \: \times 5 \times 13 \\ \\ \implies \: 65\pi \: cm {}^{2} [/tex]
_____________________________
_____________________________
( ii )
now when we flatten the cone ,
the slant height becomes the radius of the sector , while the arc becomes the circumference of cone !
[tex]\therefore \: radius = l = 13 \: cm \\ \\ arc \: length = circumference = 2\pi \: r[/tex]
now ,
[tex]s = d \: \theta \: ( \: for \: a \: sector \: ) \\ \\ \therefore \: l\theta \: = 2\pi \: r \\ \\ \implies \: \theta = \frac{2\pi \: r}{l} \\ \\ \implies \: \theta = \frac{2 \times \pi \times 5}{13} \\ \\ \implies \: \theta \: = \frac{10\pi}{13} \\ \\ \implies \theta \: = \: 0.77 \pi [/tex]
hope helpful :D
Step-by-step explanation:
i)
remember, the radius is half the diameter !
the overall surface area of a cone (base circle + "mantle", the lateral, curved surface) is
A = pi×r × (r + sqrt(h² + r²))
so, only the "mantle" or lateral curved stave area is
pi×r × sqrt(h² + r²) = pi×5 × sqrt(12² + 5²) = pi×5×sqrt(169) =
= pi×5×13 = 65×pi cm²
ii)
the length of the arc of the sector is the circumference of the circle, that was the base of the original cone.
that is
2×pi×r = 2×pi×5 = 10×pi cm
the total circumference of the large circle containing that sector is
2×pi×r' = 2×pi×sqrt(h² + r²)
as the radius r' of the circle containing the sector (representing the "mantle" of the cone) is the lateral height of the cone (the distance along its side from the base to the top). and that is per Pythagoras simply the square root of the sum of the square of the inner height and the square of the base radius.
in our case that is
2×pi×sqrt(12² + 5²) = 2×pi×13 = 26×pi cm
the angle of the sector is then 10/26 of the total of 360° for the whole circle :
360 × 10/26 = 138.4615385...°
or, if you need this in terms of pi too, remember that 360° are represented by 2×pi (the arc length of the standard circle).
2×pi × 10/26 = pi × 20/26 = pi × 10/13 =
= 0.769230769... × pi
Find the value of x.
x:12=5:8
Answers
Answer:
Since 5:8is constant with respect to x, the derivative of 5:8 with respect to x is 0.0
Step-by-step explanation:
Answer:
x = 7.5
Step-by-step explanation:
expressing the ratio as a fraction , that is
[tex]\frac{x}{12}[/tex] = [tex]\frac{5}{8}[/tex] ( cross- multiply )
8x = 60 ( divide both sides by 8 )
x = 7.5
Choose the inequality that represents the following graph.
Answers
Answer:
The correct answer is B
Step-by-step explanation:
The blue line points to the left and has a closed circle, so the value of x has to be less than or equal to -4.
Ok but... what's 6+6? i've been stuck on this forever and i can't see to find the answer. 0-0
Answers
Answer:
12
Step-by-step explanation:
Hurry pls with the answer
Answers
Answer:
C
Step-by-step explanation:
Plug in x, for example if you plug in x in 3x+1 you will get y which is 4, and the same for the rest.
whats f? 0.62(f + –6) + 6.96 = 8.2
Answers
Answer:
f=8
Step-by-step explanation:
0.62(f+(-6)+6.96=8.2
0.62(f-6)+6.96=8.2
multiply both sides by 100
0.62(f-6)*100+6.96*100=8.2*100
Refine
62(f-6)+696=820
Subtract 696 from both sides
62(f-6)+696-696=820-696
Simplify
62(f-6)=124
Divide both sides by 62
62(f-6)/62 = 124/62
Simplify
f-6=2
add 6 to both sides
f-6+6=2+6
simplify
f=8
Answer:
8
Step-by-step explanation:
1. Distribute 0.62 to each term in the parenthesis:
0.62(f) + 0.62(-6)
0.62f - 3.72 + 6.96 = 8.2
2. Add 3.72 and 6.96:
0.62f - 3.72 + 6.96 = 8.2
0.62f + 3.24 = 8.2
3. Subtract 3.24 from both sides of the equation:
0.62f + 3.24-3.24 = 8.2-3.24
0.62f = 4.96
4. Divide 0.62 by both sides to isolate f:
0.62f/0.62 = 4.96/0.62
f = 8
hope this helps!
Can someone help on these two?, Its okay if you can only do one.
Answers
Answer:
5 shaded region area = 100 - 78.5 = 21.5 sqm
6 c
Step-by-step explanation:
5. area of square = 10 x 10 = 100 sqm
area of circle = pi * r^2 = pi (5)^2 = 78.5 sqm (take pi as 3.14)
shaded region area = 100 - 78.5 = 21.5 sqm
6. for a straight line, equation is y = mx + b
m = 5, b = -12 in this case
Another teacher has a monthly salary of $2000 She spends $943 per month on rent Her monthly salary then increases by 15% What percentage of her new monthly salary does the teacher spend on rent?
Answers
Answer:
47.15%
Step-by-step explanation:
Getting a raise of 15% would increase the teacher's salary by 300. 943 of 2300 is 47.15%.
What is the explicit arithmetic sequence formula for 72, 48, 24,....?
Answers
Answer:
f(x)=x-24
Step-by-step explanation:
It is decreasing by 24. Hope this helps!
Answer:
The formula is f(x) = x-24
Step-by-step explanation:
72-24=48
48-24=24 and so on
A taste test asks people from Texas and California which pasta they prefe
brand A or brand B. This table shows the results.
Brand A
Brand B Total
Texas
80-
45
125
California
90
60
150
Total
170
105
275
9
A person is randomly selected from those tested.
What is the probability that the person is from Texas, given that the person
prefers brand A? Round your answer to two decimal places.
Answers
Using it's concept, it is found that there is a 0.4545 = 45.45% probability that the person is from Texas, given that the person prefers brand A.
What is a probability?A probability is given by the number of desired outcomes divided by the number of total outcomes.
In this problem, there are 176 people who prefer brand A, and of those 80 are from Texas, hence the probability is given by:
p = 80/176 = 0.4545.
0.4545 = 45.45% probability that the person is from Texas, given that the person prefers brand A.
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4. Maryam's average monthly expenses are $3,750. She wants to have an emergency fund that
covers 3 months of expenses saved up within the next 24 months. If she's starting with $300 in
her account, how much does she need to save each month to reach that goal?
Answers
Answer:
$456.25 each month
Step-by-step explanation:
Fund for 3 months 3750 * 3 = 11250
Start with 300 => 11250 - 300 = 10950
Within 24 months to reach 10950 => each month = 10950 / 24 = 456.25
She needs to save $456.25 each month for the next 24 months to reach her goal.
How to form an equation?Determine the known quantities and designate the unknown quantity as a variable while trying to set up or construct a linear equation to fit a real-world application.
In other words, an equation is a set of variables that are constrained through a situation or case.
Monthly expenses = $3,750
For 3 months = 3 × 3750 = $11250 need to save total.
Since she started with $300 so
11250 - 300 = $10950 need to save total.
Let's say the amount per month is x
24x = 10950
x = 456.25.
Hence "She needs to save $456.25 each month for the next 24 months to reach her goal".
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What is the midpoint for a segment with endpoints (3,5) and (7,-1)?
(10.4)
B
(5,2)
С
(1,3)
D
(4,4)
Answers
Answer:
B
Step-by-step explanation:
took the test >:)
help me asap i need help i dont understand
Answers
Answer:
∠A + ∠B = 90°
Step-by-step explanation:
Complementary angles are angles which, combined, add to 90°. Therefore, an equation displaying the relationship between two complementary angles may look like this: ∠A + ∠B = 90°.
Which one of the following statements is true about parallel lines
A. The Intersect at least twice
B. They intersect at one point
C. They intersect at more than one point
D.they never intersect
Answers
Answer:
D. They never intersect
Step-by-step explanation:
PLEASE HELP ASAP WILL GIVE BRAINLIEST !!
You are planning to join a gym. Muscles Gym costs $100 to join and $25 each month (C= 100 + 25x) and Cardio Gym costs
nothing to join and $50 each month (C = 50x).
Solve this linear system and choose the true statement below. (Look carefully at the order of the numbers in the solution.)
A.) The solution is (200, 4). This means that it will cost me $200 to go to either gym 4 times.
B.) The solution is (4, 200). This means that it will cost me $200 to go to either gym 4 times.
C.) The solution is (4, 200). This means that at 4 months of
membership, either gym will cost $200.
D.) The solution is (200, 4). This means that at 4 months of
membership, either gym will cost $200.
Answers
B) The solution is (4, 200). This means that it will cost me $200 to go to either gym 4 times.
the equations given to you were:
(C = 100 + 25x) and (C = 50x)
well, if you plug in 200 for C and 4 for x you get these equations,
200 = 100 + 25(4), and 200 = 50(x)
I solved both step-by-step below.
1. C = 100 + 25x plug in points
200 = 100 + 25(4) solve the parenthesis's
200 = 100 + 100 combine like terms
200 = 200 both sides are equal
2. C = 50x plug in points
200 = 50(4) solve the parenthesis's
200 = 200 both sides are equal
The first four numbers of a sequence are 3,9,27, and 81. If this sequence continues, what are the next two numbers?
Answers
Answer:
243 and 729
Step-by-step explanation:
next will be 81 x 3= 243
next will be 243 x 3= 729
Answer:
243 729
Step-by-step explanation:
r = common ratio = 3 means multiply each number by 3 to get the next number
3 9 27 81 (81*3 ) ( 81*3)*3
3 9 27 81 243 729
HELPPPP!!! LAST QUESTION!!!
Answers
Answer:
1/12
Step-by-step explanation:
Total students: 24
Requirement: 2
Simplify:
2/24 -> 1/12
10 more than the difference of 6m and 3. Write the sentence as a numerical expression
NEED HELP ASAP
Answers
Answer:
10 + 6 - 3
Step-by-step explanation:
What is the Trigonometric ratio of cos180?
Answers
[tex]\cos 180^{\circ}\\\\=\cos(2 \cdot 90^{\circ})\\\\=2 \cos^2 90^{\circ}-1\\\\=2 \cdot 0 - 1\\\\=0-1\\\\=-1[/tex]
hi lots of work today
Answers
Answer:
x-axis
Step-by-step explanation:
The lateral line on a graph is known as the x-axis
PLSSS I NEED HELP I’LL MARK BRAINLYESS OR WTV IS CALLED
Answers
Answer: y= -7 y= -5 y= -3 y= -1
Step-by-step explanation:
Katrina's ski boots cost 8%more than her skis.her ski boots cost $162 .Which equation can be used to find the cost c,of Katrina's skis.
A. C + 0.08c=162
B C +0.8c =162
C C+ 0.08c =162
D C+ 0.8c=162
please help me
Answers
How long is it:
a) from 18 00 until 09 45 the next day?
b) from 07 30 until 01 45 the next day?
c) from 18 50 until 09 20 the next day?
d) from 08 10 until 00 35 the next day?
Answers
Answer:
a) 15h 45m gap
b) 06h 15m gap
c) 14h 30m gap
d) 16h 25m gap
Answer:
a) 3 hours and 45 mins
b) 18 hours and 15 minmins
c) 2 hours and 30 mins
d) 16 Hours and 20 mins
I might be wrong...
The histogram below shows the estimated monthly salaries of company employees with different years of experience. a bar graph entitled estimated monthly salary has years of experience on the x-axis, and estimated monthly salary on the y-axis. with 13 to 15 years of experience, an employee makes 3,000 dollars; with 16 to 18 years, they make 4,000; with 19 to 21 years, they make 5,000. how might the graph be misleading? the scale on the y-axis overemphasizes the difference in salaries between different experience levels. the scale on the y-axis underemphasizes the difference in salaries between different experience levels. the scale on the x-axis overemphasizes the difference in salaries between different experience levels. the scale on the x-axis underemphasizes the difference in salaries between different experience levels.
Answers
The scale on the y-axis overemphasizes the difference in salaries between different experience levels.
What is a histogram?The histogram is one of the ways of data presentation. Usually, it utilizes rectangles plotted on the x and the y axis.
In this case, the graph is misleading in the sense that; the scale on the y-axis overemphasizes the difference in salaries between different experience levels.
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Answer:
A
Step-by-step explanation:
